Sound basics

Sound may be defined as any pressure variation (in air, water or any other medium) that the human ear can detect.

Knowing the speed and frequency of a sound, we can
calculate the wavelength - that is, the distance from
one wave top or pressure peak to the next.

Wavelength (Lamda) = Speed of sound / Frequency

From this equation we can work out the wavelength at
different frequencies. For example at 20 Hz one wavelength
is just over 17 meters, while at 20 kHz, it is only
1,7cm. Thus, we see high frequency sounds have short
wavelengths and low frequency sounds have long wavelengths.

A sound which has only one frequency is known as a
pure tone. In practice pure tones are seldom encountered
and most sounds are made up of different frequencies.
Even a single note on a piano has a complex
waveform. Most industrial noise consists of a wide mixture
of frequencies known as broad band noise. If the
noise has frequencies evenly distributed throughout the
audible range it is known as white noise and it sounds
rather like rushing water.

Sound basic parameters

Under free-field conditions

When sound is produced by a sound source with a sound power, P, a
transfer of energy from the source to the adjacent air molecules takes place.

This energy is transferred to outlying molecules. Thus the energy spreads
away from the source rather like ripples on a pond. The rate at which this
energy flows in a particular direction through a particular area is called the
sound intensity, I. The energy passing a particular point in the area around
the source will give rise to a sound pressure, p, at that point.

r is the density of air, c is the speed of sound.

Note that sound intensity is a vector quantity - it has magnitude as well as
direction.

Sound intensity and sound pressure can be measured directly by suitable
instrumentation. Sound power can be calculated from measured values of
sound pressure or sound intensity levels and a knowledge of the area over
which the measurements were made. The main use of sound power is for
the noise rating of machines etc. and sound intensity is mainly used for
location and rating of noise sources. When it comes to evaluation of the
harmfulness and annoyance of noise sources, sound pressure is the
important parameter.

Sound pressure

When a sound source such as a tuning fork vibrates it sets up pressure
variations in the surrounding air. The emission of the pressure variations can
be compared to the ripples in a pond coused by a stone thrown in the water.

The ripples spread out from the point where the stone entered. However the
water itself does not move away from the center. The water stays where it is,
moving up and down to produce the circular ripples on the surface. Sound is
like this. The stone is the source, the pond is the air, and the ripples are the
resulting sound wave.

dB - decibel

The advantage of using dB's is clearly seen when a dB scale is drawn on the
illustration shown earlier. The linear scale with its large and unwieldy
numbers is converted into a much more manageable scale from 0 dB at the
threshold of hearing (20 mPa) to 130 dB at the threshold of pain.

Lp = 20 log (p/p0) dB re 20 mPa

(p0 = 20 mPa = 20 × 10-6 Pa)

The sound pressure level, Lp, in dB's is defined as 20 log p/p0 , where p is
the measured value in Pa, and p0 is a standardised reference level of 20 mPa
- the threshold of hearing. Note here that the word level is added to sound
pressure to indicate that the quantity has a certain level above the reference
level, and the symbol for sound pressure level is Lp. The illustration shows
two examples of how to use the formula for calculation of dB levels. Besides
being examples of calculation, these two levels are interesting because they
are the levels used for sound level meter calibration

Sound fields

The source we looked at earlier is called a point source and for such a
source it was mentioned that the sound pressure drops to half it's value
when the distance to the source is doubled. This correspond to a drop in
sound pressure of 6 dB.

Another type of source is the line source, which could be a pipe carrying a
turbulent fluid, or a road with a high traffic flow. The sound pressure from a
line source only drops by approximately 3 dB for a doubling of distance from
the source, because the sound spreads out from the source as a wavefront
in a direction perpendicular to the line source.

The most rarely found type of sound source when dealing with normal noise
measurements is the plane source. A plane source will in principle consist of
a piston from which energy is radiated into a tube setting up a plane wave in
the tube. Assuming no loss of energy through the walls of the tube, the
intensity, i.e. the acoustic energy flowing through the tube, is independent of
the distance from the source. Since the intensity is the same everywhere in
the tube, the sound pressure level will not drop with an increase in distance
from the piston.

In practice, the majority of sound measurements are made in rooms that are
neither anechoic nor reverberant - but somewhere in between. This makes it
difficult to find the correct measuring positions where the noise emission
from a given source must be measured.

It is normal practice to divide the area around a noise source e.g. a machine
into four different fields:

Near field

Far field

Free field

Reverberant field

The near field is the area very close to the machine where the sound
pressure level may vary significantly with a small change in position. The
area extends to a distance less than the wavelength of the lowest frequency
emitted from the machine, or at less than twice the greatest dimension of the
machine, whichever distance is the greater. Sound pressure measurements
in this region should be avoided.

The far field is divided into the free field and the reverberant field.

In the free field the sound behaves as if in open air without reflecting
surfaces to interfere with its propagation. This means, that in this region the
sound level drops 6 dB for a doubling in distance from the source.

In the reverberant field, reflections from walls and other objects may be just
as strong as the direct sound from the machine.